Influence of simple and complex non-axisymmetric background magnetic fields on the propagation of QG MC waves

Magneto-Coriolis (QG-MC) waves are considered an important part of the rapid dynamics of the Earth's outer core. The detailed characteristics of these waves are however still under scrutiny. In this study we explore the sensibility of the QG-MC waves to the background magnetic field over which they propagate and to the frequency of the perturbation that can generate them in the Earth core. We retrieve QG-MC waves propagating over a realistic background magnetic field by analysing the velocity fields, where they are most easily observed. Concentrations of QG-MC waves in the magnetic field at the core surface in our model are reminiscent of recently observed geomagnetic jerks. The QG-MC waves are weakly sensitive to the details of the background magnetic field during their travel in the bulk and their frequency at the core surface remains close to that of the initial perturbation. This is a potential asset for the prediction of their evolution. Moreover, the waves in the system exhibit a complex relation with the initial perturbation: when the frequency of the initial pulsation is greater than a threshold -- depending on the Alfv\'en speed and the geometric complexity of the medium -- inward QG-Alfv\'en waves are recovered at the core mantle boundary instead of QG-MC waves, and we find a continuum of waves from QG-MC to %inertial waves QG-Alfv\'en waves depending on the input frequency. Thus, gradually increasing the input frequency in the system, we retrieve the dispersion relation for QG-MC waves with an evolution from a k_s^4 slope to a k_s^1 slope, where k_s is the cylindrical radial wavenumber, as waves transition from QG-MC to QG-Alfv\'en waves. Applying our results to the Earth's core, we expect to be able to recover QG-MC waves with confidence in the Earth core with periods between 57y and 2.8y.